In the oil and gas industry, geophysical prospecting techniques commonly are used to aid in the search for and evaluation of subterranean hydrocarbon resources. These resources are found in hydrocarbon reservoirs, which are porous bodies of rock in the subsurface where the pore space within the rock is at least partly filled by hydrocarbons. The profitability of drilling and producing hydrocarbons from a reservoir depends on both the type or types of fluid contained in the pore space of the reservoir rock, such as oil, natural gas, or ground water, and the reservoir properties of the rock, such as its porosity and permeability. In geophysical prospecting, the fluid type and reservoir properties are estimated from geophysical survey data collected at or near the surface, such as seismic data, resistivity data or gravity data.
The composition and structure of a reservoir rock and the type of fluid in the pore space of the rock influence the reflection and transmission of seismic waves by the rock and the conductivity and dielectric constant of the rock. Relationships among seismic, electrical and reservoir properties are exploited in geophysical prospecting for hydrocarbons, where data from seismic or electromagnetic surveys are used to predict the spatially-varying properties of a reservoir. The predicted reservoir properties are the basis for decisions about how many wells to drill, the type of well to drill, and where the wells should be placed to optimally recover the resource from the reservoir.
Various methods are applied to determine fluid and reservoir properties from geophysical survey data. These methods fall generally into two categories: interpretation and inversion. Interpretation methods use geophysical survey data to understand the geological structure and history of a subsurface region. From this information, an experienced interpreter can assess whether a subsurface location is likely to be a hydrocarbon reservoir. Inversion methods determine the most likely reservoir and fluid properties based on numerical models which can simulate geophysical survey data for any set of reservoir and fluid properties. In an inversion, various subsurface distributions of reservoir and fluid properties are tried until the numerical model produces simulated survey data that most nearly resembles the actual survey data. Inversion methods provide a direct estimate of those properties needed to determine the economic potential of a reservoir; however, inversion methods tend to require better quality survey data than interpretation methods and inversion estimate accuracy can depend significantly on local rock properties. In practice, both methods are usually applied when evaluating a prospective reservoir. The present inventive method is an inversion method.
The components of an inversion are generally geophysical survey data, an earth model, a rock physics model, a geophysical forward model, and an objective function. The speed and accuracy of the inversion depends on the choice of these components. These components are now described in greater detail. Geophysical survey data refers to measurements collected at points along a line or over an area at, near or above the surface of the earth and which sense properties of the subsurface. Examples of geophysical surveys include seismic surveys which sense the seismic wave velocities and density in the subsurface, magnetotelluric (MT) surveys or controlled-source electromagnetic (CSEM) surveys which sense the electrical resistivity of the subsurface, and gravity surveys which sense the density of the subsurface. Passive seismic surveys are another kind of geophysical survey where seismic wave velocities and density in the subsurface are sensed using naturally occurring seismic sources such as microseismicity or earthquakes instead of active seismic sources. The form of seismic, MT, and CSEM survey data is one or more digital data files. Seismic data, for example, are typically digitally sampled time series from each hydrophone or geophone where the amplitude of each sample corresponds to the strength of a subsurface reflection and the time of each sample corresponds to the depth of the subsurface feature that produced the reflection. The form of gravity survey data is typically a digitally sampled time series where each sample corresponds to the perturbation in the earth's gravitational field due to density variations in the area below the gravimeter while the gravimeter is moved along a survey line. Each type of geophysical survey data responds in a unique way to subsurface rock and fluid properties. Data from more than one type of geophysical survey can be processed together in a joint inversion to form a more accurate estimate of rock and fluid properties by exploiting the complementary information in differing data types.
The earth model is the framework used to represent the subsurface properties. The specific values of the properties throughout the earth model are determined from the geophysical survey data. In common practice, the earth model divides a subsurface region into cells and gives a value for each rock and fluid property in each cell. Some earth models specify a probability distribution or statistics of a probability distribution rather than a single value for each rock and fluid property in each cell. The selection of cell size is a challenge in creating earth models. In sedimentary basins, where hydrocarbon reservoirs are found, the subsurface is composed of various rock types, often in layers. A hydrocarbon reservoir may be composed of several layers of permeable rock (such as a sandstone or permeable limestone) which contain the hydrocarbons and are separated by layers of impermeable rock (such as a shale or impermeable limestone). These rock layers are often thinner than the vertical resolution of the geophysical survey. Thus each sample in the survey data is sensing an “effective” property of the subsurface that averages together the properties of several or more layers. If the earth model uses a fine grid of cells to capture the individual layer properties, the cells can be so small compared to the resolution of the survey data that their properties cannot be uniquely determined from the data. If the earth model uses a coarse grid of cells to capture effective properties at the resolution scale of the survey data, it can be difficult to isolate the fluid type and rock properties of the permeable reservoir from an effective property value which averages permeable and impermeable layers.
Rock physics models relate the rock and fluid properties of the reservoir to the geophysical properties sensed by the geophysical survey data. Unlike the earth model, in which numerical values of one or more geophysical properties are specified on a discrete grid, the rock physics model describes the relationship between the reservoir rock/fluid properties and the geophysical properties. This can be mathematical relationships in analytical form or qualitative trends reflected in nonparametric form. Most rock physics models relate the bulk properties of a rock (such as stiffness, elastic moduli, density, seismic wave velocities, resistivity, conductivity, or permeability) to the composition of the rock, expressed as the volume fractions of the material phases (both grain types and pore types) that make up the rock. Reservoir rocks are typically sedimentary rocks composed of several different material phases. For example, in a siliciclastic rock, the phases might be grains of various mineral types (e.g., quartz or feldspar) and various size ranges, as well as cements of various mineral types (e.g., quartz or calcite) which bind the grains together, pore spaces between the grains, and clay or shale that may fully or partly fill the pore spaces or may form layers in the rock. In a carbonate rock, the phases might be for example one or more types of shell fragments, skeletal remains, microporous regions, vugs, and intergranular pores. Rocks of a common origin will typically contain the same phases, though the volume fractions of the phases may vary.
In general, there would be no consistent relationship between the bulk properties of a rock and its composition, since different rock microstructures can produce different bulk properties from the same phase volume fractions. However, rocks with a common origin and history tend to have a similar microstructure so that consistent trends between bulk properties and phase volume fractions are found among such genetically related rocks. There are two classes of models applied to represent these trends. Empirical models are generally determined by a linear regression of measured bulk properties and measured phase volume fractions. Theoretical models are based on effective medium theories, but generally still have empirical parameters that must be calibrated to fit rock property measurements. For both model classes, the calibration measurements may come from well log data or laboratory measurements on rock samples, and in both cases, the depth interval in the log or the samples used must be genetically related rocks for consistent trends to be found. Ideally the data should come from the reservoir of interest, so that the trends discovered are those found in the reservoir. However, in practice, logs or samples are often taken from a geological analog of the reservoir, that is, a different but geologically similar body of rock.
The geophysical forward model predicts the geophysical survey data from the geophysical properties of the subsurface. In a forward model, a wave propagation equation is solved numerically, on a discrete computational grid using a computer, to simulate the measured survey data. Input quantities include the given earth model and the excitation source signal. The predicted geophysical responses can subsequently be compared against the measured responses. The error between the computed and the measured responses may then be used to update the earth model parameters. Geophysical forward models range in accuracy and computational speed. For example, a simple seismic forward model assumes that the reflection amplitude in stacked seismic data depends on the difference in acoustic impedance (compressional wave velocity times density) between rock layers. This model ignores the variation in reflection amplitude with angle, but is very fast to compute. A more accurate geophysical forward model relates the amplitudes of partial stacks, that is, stacks of seismic data traces within separate offset ranges such as “near” offsets from 0 to 2000 m and “far” offsets from 2000 m to 4000 m. Partial stacks give averaged reflection amplitudes over distinct offset or reflection angle ranges. These averaged amplitudes may be related to the compressional and shear wave velocities and densities above and below a reflecting interface between rock layers, where the reflection amplitude may be based on either the approximate but simpler Aki-Richards equations or the more accurate but more complicated Zoeppritz equations. Still more accurate, the forward model may relate the amplitude at every offset in a common mid-point seismic data gather to the compressional and shear wave velocities and densities above and below the reflecting interface based on either Aki-Richards equations or Zoeppritz equations. This model retains more of the information about seismic properties than the full-stack or partial-stack model, but at the cost of operating on a larger (unstacked) data set. The most accurate forward models involve a wave propagation simulation on a 3-dimensional model of compressional and shear velocities and densities, however such models require significant computational time and so are not often used in the analysis of geophysical survey data.
A limitation of most inversion methods is that they do not incorporate a statistical description of the difference between geophysical model predictions and the geophysical measurements, even though this model error can have spatial and temporal correlations and amplitude variations that must be considered in order to form an optimal estimate of the subsurface properties from the data. The minority of inversion methods that use a statistical measurement noise model apply an overly simple model which does not capture the correlations in the noise found in real data.
The most commonly used objective function for seismic inversion is least squares, where the subsurface properties are found for which the squared difference between the simulated survey data and the actual survey data is minimized. Alternatively, other functions of the difference between the simulated and actual survey data are minimized. Preferentially, the objective function should account for the likelihood of the given subsurface properties as well as the simple magnitude of the differences in the simulated and actual survey data.
A further limitation of current inversion techniques is that since they do not compute posterior probability distributions or any function of those distributions, they cannot provide error statistics of their estimates. This is a significant limitation since assigning correct uncertainties to the fluid and reservoir property predictions is essential to quantifying the financial risks of developing the reservoir.
Rock physics models are approximate relationships. They do not exactly predict the bulk properties of the rock from its composition. Error in the rock physics models introduces a certain amount of uncertainty into the prediction of reservoir properties from geophysical data. A limitation of the rock physics models used in current practice is that they do not contain a statistical description of the model uncertainty.
Geophysical data sets are commonly very large. One common practice in processing geophysical data is to reduce a geophysical data set to one or more smaller data sets which are functions of the original data set. These smaller data sets are sometimes called “attributes” of the original data set. Examples of typical attributes include the amplitude of the near offset reflection at each subsurface location, the amplitude of the far offset reflection at each subsurface location, the curvature of the reflected wavelet from a subsurface horizon of interest, etc. The function used to form the attributes is commonly determined empirically by forming trial attributes and evaluating which attributes best correlate with the subsurface properties of interest. The attribute or attributes selected by this empirical process may not capture all the information in the original data set about the subsurface properties of interest. Accordingly, there is a need for a method of selecting attributes which optimally captures information about the subsurface properties of interest.
From the foregoing, it can be seen that there is a need in hydrocarbon exploration for a method of accurately and quickly determining subsurface properties from geophysical survey data. Preferably, such a method should utilize an earth model which can be uniquely determined from the geophysical survey data yet directly specifies the fluid and rock properties of the reservoir, should utilize rock physics models that incorporate true physical constraints without making geometrical approximations regarding rock microstructure, should take into account the uncertainty in the rock physics constraints and the noise in the geophysical data, should operate on pre-stack gathers so that information is not lost by stacking or partial stacking, should output attributes or property estimates that minimize a function of the expected property error not the data consistency, and should output the uncertainty in the property estimates. The present invention satisfies this need.